Recent lattice QCD calculations show strong indications that the chiral crossover of QCD at zero baryon chemical potential \mu_B is a remnant of the second-order chiral phase transition. Furthermore, the non-universal parameters needed to map temperature T and \mu_B to the universal properties of the second-order chiral phase transition have been determined recently. Motivated by these observations, first, we determine the analytic structure of the partition function -- the so-called Yang-Lee edge singularity -- in the QCD crossover regime, solely based on universal properties. Next, utilizing the lattice QCD results for non-universal parameters we map this singularity to the real T and complex \mu_B plane, leading to the determination of the radius of convergence in \mu_B in the QCD crossover regime. These universality- and QCD-based results provide tight constraints on the range of validity of the lattice QCD calculations at \mu_B>0. The implication of this result on the location of the conjectured QCD critical point is discussed.